I would use the twenty. I always feel like I'm stressing out the fish even more when I put it in a small QT tank. Also depends a little on the size of the fish and how long they will be staying in the QT tank.
I agree, the 20G would definately be the better choice, especially since a majority of SW fish are wild-caught and therefore not used to being in such a small, enclosed space. I would also recommend putting in some sort of shelter (ie. flower pot, pvc pipe) so the fish has somewhere to take cover and feel more secure. Other than that, the tank should be bare (no sand, LR, etc.).
You will need...
-filter
-powerhead
-heater
-test kit (pH, ammonia, nitrate, nitrite)
-airstone (optional)
As you probably know you should keep your new/sick fish in the QT for at least two weeks or until any illness is cleared, checking water parameters regularily. *Important note: If a new fish shows signs of sickness after (ie. a week into) quarantine, then you should treat the problem accordingly and
begin the two week period all over again.
Oh and remember not to use carbon in the filter, as carbon will remove any medication from the water.
Regarding your question on temperature, as far as I know the QT temperature requirements are the same as the display tank (72 - 78°F), but you should look into it if you're unsure.
Hope this helps